List of top Mathematics Questions on Differential equations asked in MET

Order and degree of a differential equation \(\frac{d^2y}{dx^2} = \left\{ y + \left(\frac{dy}{dx}\right)^2 \right\}^{1/4}\) are

If \(m\) parallel lines in a plane are intersected by a family of \(n\) parallel lines, then the number of parallelograms that can be formed is

A person is permitted to select at least one and at most \(n\) coins from a collection of \((2n+1)\) distinct coins. If the total number of ways in which he can select coins is 255, then \(n\) equals

\((\sim p \wedge q)\) is logically equivalent to

The solution of the differential equation \( \frac{dy}{dx} - \sin x \sin y = 0 \) is

The differential equation satisfied by the family of curve \( y = ax \cos \left( \frac{1}{x} + b \right) \), where \( a, b \) are parameters, is:

Integrating factor of the equation: \[ (x^2 + 1) \frac{dy}{dx} + 2xy = x^2 - 1 \] is:

The function \( f(x) = \frac{ax + b}{(x-1)(x-4)} \) has a local maxima at \( (2, -1) \), then

If \( x^y = e^{x - y} \), then \( \frac{dy}{dx} \) is equal to

The area of the loop of the curve $ay²=x²(a-x)$ is

Solution of the differential equation \[ x = 1 + xy \frac{dy}{dx} + \frac{(xy)^2}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!} \left(\frac{dy}{dx}\right)^3 + \cdots \] is

The solution of the differential equation \( \frac{dy}{dx} = \sin(x+y)\tan(x+y) - 1 \) is

The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

The solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) is: